Combined in-plane and through-the-thickness analysis for failure prediction of bolted composite joints

Although two-dimensional methods provide accurate predictions of contact stresses and bolt load distribution in bolted composite joints with multiple bolts, they fail to capture the effect of thickness on the strength prediction. Typically, the plies close to the interface of laminates are expected to be the most highly loaded, due to bolt deformation, and they are usually the first to fail. This study presents an analysis method to account for the variation of stresses in the thickness direction by augmenting a two-dimensional analysis with a one-dimensional through the thickness analysis. The two-dimensional in-plane solution method based on the combined complex potential and variational formulation satisfies the equilibrium equations exactly, and satisfies the boundary conditions and constraints by minimizing the total potential. Under general loading conditions, this method addresses multiple bolt configurations without requiring symmetry conditions while accounting for the contact phenomenon and the interaction among the bolts explicitly. The through-the-thickness analysis is based on the model utilizing a beam on an elastic foundation. The bolt, represented as a short beam while accounting for bending and shear deformations, rests on springs, where the spring coefficients represent the resistance of the composite laminate to bolt deformation. The combined in-plane and through-the-thickness analysis produces the bolt/ hole displacement in the thickness direction, as well as the stress state in each ply. The initial ply failure predicted by applying the average stress criterion is followed by a simple progressive failure. Application of the model is demonstrated by considering single- and double-lap joints of metal plates bolted to composite laminates.